$\dfrac{ -3q - 9r }{ 8 } = \dfrac{ 6q + 9s }{ -5 }$ Solve for $q$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -3q - 9r }{ {8} } = \dfrac{ 6q + 9s }{ -5 }$ ${8} \cdot \dfrac{ -3q - 9r }{ {8} } = {8} \cdot \dfrac{ 6q + 9s }{ -5 }$ $-3q - 9r = {8} \cdot \dfrac { 6q + 9s }{ -5 }$ Multiply both sides by the right denominator. $-3q - 9r = 8 \cdot \dfrac{ 6q + 9s }{ -{5} }$ $-{5} \cdot \left( -3q - 9r \right) = -{5} \cdot 8 \cdot \dfrac{ 6q + 9s }{ -{5} }$ $-{5} \cdot \left( -3q - 9r \right) = 8 \cdot \left( 6q + 9s \right)$ Distribute both sides $-{5} \cdot \left( -3q - 9r \right) = {8} \cdot \left( 6q + 9s \right)$ ${15}q + {45}r = {48}q + {72}s$ Combine $q$ terms on the left. ${15q} + 45r = {48q} + 72s$ $-{33q} + 45r = 72s$ Move the $r$ term to the right. $-33q + {45r} = 72s$ $-33q = 72s - {45r}$ Isolate $q$ by dividing both sides by its coefficient. $-{33}q = 72s - 45r$ $q = \dfrac{ 72s - 45r }{ -{33} }$ All of these terms are divisible by $3$ Divide by the common factor and swap signs so the denominator isn't negative. $q = \dfrac{ -{24}s + {15}r }{ {11} }$